Question: Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?
Explanation: There are two segments of Brenda's trip: from $(-4,5)$ to $(0,0)$, and from $(0,0)$ to $(5,-4)$. Using the distance formula, the total distance is  \begin{align*}
\sqrt{(-4-0)^2+(5-0)^2}&+\sqrt{(5-0)^2+(-4-0)^2}\\
&=\sqrt{16+25}+\sqrt{25+16}\\
&=\boxed{2\sqrt{41}}.
\end{align*}